You can proceed with amending your Federal return and wait to see the resolution of your open case with the state before amending the state return. You are not required to amend the state return if it's the same issue and it's resolved without an amendment, or if there would not be a change to your return if you did file an amendment.
It might be easier to wait until the state case is resolved, just in case they find something else you overlooked, but if you end up owing the IRS because of the additional W-2, you want to be sure to file and pay "on time" that is, by April 15th.
